(geomview-pt_BR)Geometrias Nao-Euclidianas

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8 Geometrias Na~o-Euclidianas
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Geomview supports hyperbolic and spherical objeto geome'trico as well as
Euclidean objeto geome'trico.  The three boto~es at the bottom do _Main_
panel are for setting the current objeto geome'trico type.

   In each das three geometries, three models are supported: _Virtual_,
_Projective_, and _Conformal_.  You can change the current model with
the _Model_ browser on the _Camera_ panel.  Each Geomview ca^mera has
its own model setting.

   The default model is all three spaces is _Virtual_.  This
corresponds to the ca^mera being in the same space as, and moving under
the same set of transformations as, the objeto geome'trico itself.

   In Euclidean space _Virtual_ is the most useful model.  The other
models were implemented for hyperbolic and spherical spaces and just
happen to work in Eucldiean space as well: _Projective_ is the same as
_Virtual_ but by default displays the unit sphere, and _Conformal_
displays everything inverted in the unit sphere.

   In hyperbolic space, the _Projective_ model setting gives a view do
projective ball model of hyperbolic 3-space imbedded in Euclidean
space.  The ca^mera is initially outside the unit ball.  In this model,
the ca^mera moves by Euclidean movimentos and objeto geome'trico moves
by hyperbolic movimentos.  _Conformal_ model is similar but shows the
conformal ball model instead.

   In spherical space, the _Projective_ model gives a view of half da
3-sphere imbedded in Euclidean 3-space.  Spherical movimentos give rise
to projective transformations in the _Projective_ model, and to Moebius
transformations in the _Conformal_ model.  In both of these models the
ca^mera moves by Euclidean movimentos.

   In _Projective_ and _Conformal_ models, the unit sphere is drawn by
default.  You can turn it off and on at will using the _Draw Sphere_
bota~o in the _Camera_ panel.  In the _Conformal_ model, poli'gonos and
edges are subdivided as necessary to make them look curved.  The
parameters which determine this subdivision can be set with the
`set-conformal-refine' GCL command. *Note `(set-conformal-refine ...)':
set-conformal-refine.

   There are several sample hyperbolic space objetos in the
`data/geom/hyperbolic' subdirectory do Geomview directory.  Likewise,
the subdirectory `data/geom/spherical' contains several sample
spherical space objetos.